Abstract. A variant of Cauchy mean-value theorem is presented. Applying a counterpart of the Lagrange mean-value theorem, we introduce new type of means. The functions generating the homogeneous means of this type are determined. In some special cases the effective formulas for these means are presented. Mean-value-theorems which do not lead to any mean are also mentioned.Mathematics subject classification (2010): Primary 26A24; Secondary 39B22.
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